Question: Differential equation

Find the solution(s) of the differential equation E=(1+x^2)*(dy/dx)^2+y(x)^2, when E=1 and the initial condition y(0)=0 is imposed.

Plot your solutions oner the range 0<=x<=12, also plot y against log(x) for 1<=x<=10^4. Comment on the number of solutions obtained and their relation to each other.

Find the first three zeros of y(x) to 2.s.f (that is, xc such that y(xc)=0)

 

My solution:

E:=(1+x^2)*(diff(y(x),x))^2+(y(x))^2;

dsolve({E=1,y(0)=0},y(x));

Then my problem is the other parts of the question! While trying to plot the solutions using the plot command, maple took like 7 minutes to plot them and when I tried to plot the two solutions against log(x), I had an error saying:  Warning, unable to evaluate 2 of the 3 functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

Also I after tried to use the ode command but I also had an error!

Can someone please tell me how to plot the solutions of the diff.equation over the range 0<=x<=12 and then how to plot y against log(x) for 1<=x<=10^4??  I suspect logx against y, means the two solutions with the graph of logx on the same axes. Also the last part of the question don't know how to solve it with Maple.

Thanks in advance for any help! Appreciate it

 

Kidn regards!

 

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